Their intervention has received the backing of the Archbishop of Canterbury and the Archbishop of York.

The government says the reforms are designed to reduce a culture of benefit dependency.

The bishops say the cap could be "profoundly unjust" to children in the poorest families and they have a "moral obligation to speak up for those who have no voice".

They are backing a series of amendments to the Welfare Reform Bill - due to be debated in the House of Lords on Monday - which have been tabled by the Bishop of Ripon and Leeds, Rt Rev John Packer.

'Falling into poverty'

He told the BBC: "It is unusual for a very considerable number of bishops to come together and to sign a letter, and we do consider we have a very particular concern for children and to prevent children from falling into poverty.

"The bill as it stands looks to us as though it could cause very considerable damage to children - particularly those in larger families, it being no fault of the children that they're in larger families."

The government says the changes, due to come into effect in 2013, will save £7bn in welfare spending and will encourage people currently on benefits to go out and find a job.

It simply isn't fair that households on out-of-work benefits can receive a greater income from the state than the average working household gets in wagesDepartment for Work and Pensions

But the Children's Society, which supported the bishops' letter, has warned the cap could make more than 80,000 children homeless.

It has proposed the bill should be amended to remove child benefit from the calculations for household income.

For Labour, shadow chancellor Ed Balls said it supported efforts to get people back to work and believed welfare should not be open-ended.

But he said the government's approach was flawed and suggested Communities Secretary Eric Pickles had warned it could lead to 40,000 people having to leave their homes.

"The bishops have got a point," he told Sky News. "I don't think the government have designed this at all well. Let's not do this in a way which hurts the poorest by throwing them out of their homes."

London rent

Earlier this month, church leaders in Northern Ireland warned that the reforms would push vulnerable people into "precarious levels of poverty".

It is estimated the cap, which would apply to the combined income from benefits such as jobseekers' allowance, housing benefit and council tax benefit, could result in about 50,000 families being about £93 a week worse off.

London is expected to be one of the worst affected areas, because of the high cost of renting in the capital.

Earlier this week, a study on behalf of London Councils said about 133,000 households in London would be unable to afford their rent if the proposed changes went ahead.

A spokesman for the Department for Work and Pensions said the proposed cap would be the equivalent of an annual salary of £35,000 a year before tax.

"It simply isn't fair that households on out-of-work benefits can receive a greater income from the state than the average working household gets in wages," he said.

"Many working-age families with adults in work cannot afford to live in central London, for example, and it is not right for the taxpayer to subsidise households on out-of-work benefits who do."